Abstract
Because of shorter key and higher security, elliptic curve cryptosystem has attracted people’s attention and it is widely used in various fields, such as wireless sensor networks. Scalar multiplication is one of the most basic and critical links in the realization of elliptic curve public key systems, and its operation efficiency directly affects the implementation efficiency of the entire cryptographic system. To improve speed up the efficiency of the scalar multiplication algorithm, we express $k $ for scalar multiplication $kP $ by using triple-base chain representation of the scalar using $\{2,3,7\} $ as basis of the triple-base chain in this paper. However, the efficiency of scalar multiplication is not only related to the length of representation but also the numbers and costs of doubling, tripling, septupling and addition. Therefore, we improve septuple formula of the elliptic curve by using Co_Z operation, which costs decreased by 8.3%. Due to the high redundancy of the triple-base chain representation, the algorithm can resist side channel attacks. The experimental results show that the proposed algorithm compared with that of other scalar multiplication algorithms, it requires less cost.
Highlights
The security of Elliptic curve cryptography (ECC) depends on the computational intractability of the elliptic curve discrete logarithm problem (ECDLP)
CONTRIBUTION In the present work, our main contributions are as follows: First, we improve septuple formula of the elliptic curve by using Co_Z operation, which costs decreased by 8.3%
The elliptic curve cryptographic algorithm is one of the most widely used public key cryptographic algorithms, and the performance of the scalar multiplication operation is key to its application
Summary
W ITH the rapid development of wireless communication technology, wireless sensor networks of lowcost, low-power, and multi-functionalare is used in many civilian fields, such as environmental and ecological monitoring, health monitoring, home automation, and traffic control.users have high requirements for the security capabilities of wireless sensor networks in these application environments. Since the length of the TBC representation has not been visibly became short, but the number of points doublings, point triplings, and point septuplings increased greatly, the computational overhead of scalar multiplication may be very large. It is of great significance for TBC to optimize to reduce the computational complexity of the underlying filed by improving operation on the bottom layer such as field inverse, multiplication and so on. An efficient scalar multiplication algorithm of a point P on an elliptic curve is proposed using TBC representation of the scalar using {2, 3, 7} as basis of the TBC.
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